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Re: NSolve Vs. Elliptic Integral

• To: mathgroup at smc.vnet.net
• Subject: [mg62500] Re: [mg62471] NSolve Vs. Elliptic Integral
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 26 Nov 2005 02:46:56 -0500 (EST)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

NSolve is intended primarily for polynomials (see Help browser).  Use 
FindRoot.

Clear[f,g];

f[x_,m_]:=Sqrt[(1+0.176*Sin[m]^2*Sin[x]^2)*
        (1+1.018*Sin[m]^2*Sin[x]^2)/(1-Sin[m]^2*Sin[x]^2)];

g[m_]:=0.159*Sqrt[1/(-9*10^(-6)+Sin[m]^2)];

FindRoot[
  NIntegrate[f[x,m],{x,ArcSin[0.003/Sin[m]],Pi/2}]==g[m],
  {m,1}]

{m -> 0.102762168294469}

Plot[{NIntegrate[f[x,m],{x,ArcSin[0.003/Sin[m]],Pi/2}],g[m]},
    {m,0.05,.15},PlotStyle->{Blue,Red},Frame->True,Axes->False];


Bob Hanlon

> 
> From: "nilaakash at gmail.com" <nilaakash at gmail.com>
To: mathgroup at smc.vnet.net
> Date: 2005/11/25 Fri AM 02:25:24 EST
> Subject: [mg62500] [mg62471] NSolve Vs. Elliptic Integral
> 
> Dear Friends,
>                        I am facing a problem to NSolve an  Elliptic
> Integral like that.
> 
> f[x_] := Sqrt[(1 +
>           0.176*Sin[m]^2*Sin[x]^2)*(1 + 1.018*Sin[m]^2*Sin[x]^2)/(1 -
>             Sin[m]^2*Sin[x]^2)]
> 
> g[m] = 0.159*Sqrt[1/(-9*10^(-6) + Sin[m]^2)];
> 
> NSolve[NIntegrate[f[x], {x, ArcSin[0.003/Sin[m]], Pi/2}] == g[m], m]
> 
> 
> Here I want to get an "m" value such that integration value = g[m].
> 
> This NSolve shows problem, please could any body tell me how to get
> exact m value.
> 
> Thanks.
> 
> nilaakash
> 
> 

• Follow-Ups:
  • Re: Re: NSolve Vs. Elliptic Integral
    • From: Pratik Desai <pdesai1@umbc.edu>